# Efficient Vertex-Label Distance Oracles for Planar Graphs

@article{Mozes2017EfficientVD,
title={Efficient Vertex-Label Distance Oracles for Planar Graphs},
author={Shay Mozes and Eyal E. Skop},
journal={Theory of Computing Systems},
year={2017},
volume={62},
pages={419-440}
}
• Published 2017
• Mathematics, Computer Science
• Theory of Computing Systems
We consider distance queries in vertex-labeled planar graphs. For any fixed 0 < 𝜖 ≤ 1/2 we show how to preprocess a directed planar graph with vertex labels and arc lengths into a data structure that answers queries of the following form. Given a vertex u and a label λ return a (1 + 𝜖)-approximation of the distance from u to its closest vertex with label λ. For a directed planar graph with n vertices, such that the ratio of the largest to smallest arc length is bounded by N, the preprocessing… Expand
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